I'm working on Example 4, page 262, of Harris Hancock's book which reads: Prove that 1/(sn(iu,k))^2 + 1/(sn(u,k))^2 = 1. I can only get this result if sn(u,k)=sn(u,k'), where k' is the complimentary modulus of k. But that does not make sense.

I'm working on Example $4$, page $262$, of Harris Hancock's book Lectures on the Theory of Elliptic Functions which reads:

Prove that $\dfrac{1}{\operatorname{sn}(iu,k)^2} + \dfrac{1}{\operatorname{sn}(u,k)^2} = 1$.

I can only get this result if $\operatorname{sn}(u,k) = \operatorname{sn}(u,k')$, where $k'$ is the complimentary modulus of $k$. But that does not make sense.